Volume 111, Issue 10, Pages 2077-2085 (November 2016) Sizes of Long RNA Molecules Are Determined by the Branching Patterns of Their Secondary Structures  Alexander Borodavka, Surendra W. Singaram, Peter G. Stockley, William M. Gelbart, Avinoam Ben-Shaul, Roman Tuma  Biophysical Journal  Volume 111, Issue 10, Pages 2077-2085 (November 2016) DOI: 10.1016/j.bpj.2016.10.014 Copyright © 2016 Biophysical Society Terms and Conditions

Figure 1 Schematics of an RNA molecule as a branched polymer. (A) Minimum free energy secondary structure with the maximum ladder path highlighted in magenta and flexible joints or branch points as blue dots. (B) Tree graph representation of the secondary structure in (A), with illustration of the partitioning into two halves (L1(j) and L-L1(j)) at bond j for Rg computation using the Kramers theorem (see Materials and Methods). (C) An experimentally determined secondary structure of segment 11 (60) with maximum ladder path highlighted, and experimental MLDexp and predicted 〈MLD〉 compared. (D) A representative secondary structure prediction for MS2 genomic RNA and predicted 〈MLD〉. To see this figure in color, go online. Biophysical Journal 2016 111, 2077-2085DOI: (10.1016/j.bpj.2016.10.014) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 2 (A) Measured Rh as a function of nucleotide length (in kb). Numbering of RNAs is according to their increasing length (Table 1) and coloring is according to the class (black, single-stranded precursors of dsRNA viral genomes; red, genomes of ssRNA viruses; blue, cellular mRNAs; green, ribosomal RNA; and cyan, long noncoding RNAs. Lines and curves represent best fits to different linear polymer models: charged (red, Eq. 1, ν = 1, reduced χ2 = 35.85), simple Gaussian coil (blue, Eq. 1, ν = 0.5, reduced χ2 = 13.37), and a self-avoiding coil (green, Eq. 1, ν = 0.59, reduced χ2 = 14.85). (B) Correlation between Rh and Rg predicted from 〈MLD〉 (in bp units); solid line is the best fit with reduced χ2 = 11.28. (C) Correlation between Rh and Rg predicted from Kramers theorem (in units of the average segment length, a.u.); solid line is the best fit with reduced χ2 = 12.74. RNA color coding and numbering is the same as in (A). Error bars were omitted for clarity; see Table 1 for standard deviations. To provide directly comparable reduced χ2 values, all fitting was performed using the same nonlinear Levenberg-Marquardt algorithm in OriginPro (OriginLab, Northampton, MA). To see this figure in color, go online. Biophysical Journal 2016 111, 2077-2085DOI: (10.1016/j.bpj.2016.10.014) Copyright © 2016 Biophysical Society Terms and Conditions

Figure 3 Hydrodynamic size reduction in the presence of Mg2+ (A) or spermidine Sp3+ (B). Coloring and numbering scheme is as in Fig. 2. Rh values that were compromised by either quenching or possible aggregation (RV s1 and s11 in Table 1) in the presence of multivalent cations were omitted from the plot. Linear regression lines with slopes 0.77 ± 0.03, Pearson’s r = 0.89 for Mg2+ and 0.73 ± 0.04, and Pearson’s r = 0.87 for Sp3+, respectively, are shown. To see this figure in color, go online. Biophysical Journal 2016 111, 2077-2085DOI: (10.1016/j.bpj.2016.10.014) Copyright © 2016 Biophysical Society Terms and Conditions